Logarithm Algebra (Power Property) - To Quadratic (Coefficient 1)

Level 1

This math topic focuses on applying the power property of logarithms to simplify expressions and form quadratic equations. In each problem, a logarithmic equation is presented, and users are required to simplify it into a quadratic form with the coefficient 1. The problems involve variables represented by different letters, and the tasks emphasize using the logarithm power rule to re-express given equations to find the value of the variables involved. Multiple choice answers are provided for students to select from after simplifying the logarithmic expressions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Logarithm Algebra (Power Property) - To Quadratic (Coefficient 1) Worksheet

Logarithm Algebra (Power Property) - To Quadratic (Coefficient 1)

Use the power rule to simplify this to an equation with variable 'z'

$A LaTex expression showing 2\log sub 2 (z + 1) = \log sub 2 (4)$

A LaTex expression showing (z + 2) = 16

A LaTex expression showing (z + 1) to the power of 2 = 16

A LaTex expression showing 2(z + 1) = 16

Use the power rule to simplify this to an equation with variable 't'

$A LaTex expression showing 2\log sub 7 (t - 8) = \log sub 7 (4)$

A LaTex expression showing (t - 16) = 16

A LaTex expression showing 2(t - 8) = 16

A LaTex expression showing (t - 8) to the power of 2 = 16

Use the power rule to simplify this to an equation with variable 'w'

$A LaTex expression showing 3\log sub 5 (w + 9) = \log sub 5 (4)$

A LaTex expression showing (w + 27) = 64

A LaTex expression showing (w + 9) to the power of 3 = 64

A LaTex expression showing 3(w + 9) = 64

Use the power rule to simplify this to an equation with variable 'w'

$A LaTex expression showing 2\log sub 4 (w - 3) = \log sub 4 (4)$

A LaTex expression showing 2(w - 3) = 16

A LaTex expression showing (w - 6) = 16

A LaTex expression showing (w - 3) to the power of 2 = 16

Use the power rule to simplify this to an equation with variable 'x'

$A LaTex expression showing 3\log sub 6 (x - 5) = \log sub 6 (1)$

A LaTex expression showing 3(x - 5) = 1

A LaTex expression showing (x - 15) = 1

A LaTex expression showing (x - 5) to the power of 3 = 1

Use the power rule to simplify this to an equation with variable 'r'

$A LaTex expression showing 2\log sub 8 (r - 6) = \log sub 8 (9)$

A LaTex expression showing (r - 12) = 81

A LaTex expression showing (r - 6) to the power of 2 = 81

A LaTex expression showing 2(r - 6) = 81

Use the power rule to simplify this to an equation with variable 'q'

$A LaTex expression showing 2\log sub 6 (q - 1) = \log sub 6 (4)$

A LaTex expression showing (q - 2) = 16

A LaTex expression showing (q - 1) to the power of 2 = 16

A LaTex expression showing 2(q - 1) = 16

Use the power rule to simplify this to an equation with variable 'y'

$A LaTex expression showing 2\log sub 6 (y + 8) = \log sub 6 (1)$

A LaTex expression showing (y + 8) to the power of 2 = 1

A LaTex expression showing (y + 16) = 1

A LaTex expression showing 2(y + 8) = 1